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This study marks a pivotal milestone by successfully executing an end-to-end quantum error correction pipeline to compute molecular hydrogen's ground-state energy on the Quantinuum H2-2 processor. By integrating Steane QEC gadgets and partially fault-tolerant techniques, the team achieved high-fidelity results within 0.0013 hartree of the exact solution, demonstrating that real-time error correction can effectively manage complex circuitry. Future progress hinges on optimizing protocols for memory noise protection to further enhance computational stability in chemical simulations.
Quantum Error-Corrected Computation of Molecular Energies
arXiv:2505.09133v3 Announce Type: replace Abstract: We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $[[7,1,3]]$ color code on Quantinuum H2--2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant (FT) techniques for the Clifford+$R_{Z}$ (arbitrary-angle single-qubit rotation) gate set, and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits' performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (mid-circuit measurements), and $\sim$3900 ($\sim$760) total operations are applied on average. The energy $E$ is experimentally estimated to within $E - E_{\mathrm{FCI}} = 0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols towards higher memory noise protection is the most promising avenue to improve our experimental results.
Authors:Kentaro Yamamoto, Yuta Kikuchi, David Amaro, Ben Criger, Silas Dilkes, Ciarán Ryan-Anderson, Andrew Tranter, Joan M. Dreiling, Dan Gresh, Cameron Foltz, Michael Mills, Steven A. Moses, Peter E. Siegfried, Maxwell D. Urmey, Justin J. Burau, Aaron Hankin, Dominic Lucchetti, John P. Gaebler, Natalie C. Brown, Brian Neyenhuis, David Muñoz Ramo
Abstract:We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $[[7,1,3]]$ color code on Quantinuum H2--2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant (FT) techniques for the Clifford+$R_{Z}$ (arbitrary-angle single-qubit rotation) gate set, and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits' performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (mid-circuit measurements), and $\sim$3900 ($\sim$760) total operations are applied on average. The energy $E$ is experimentally estimated to within $E - E_{\mathrm{FCI}} = 0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols towards higher memory noise protection is the most promising avenue to improve our experimental results.
arXiv:2505.09133 [quant-ph]
(or arXiv:2505.09133v3 [quant-ph] for this version)
https://doi.org/10.1103/m7j3-5sk6 DOI(s) linking to related resources
Full text under the publisher's open licence · 254 words
